In this paper, a new representational model is introduced for the rational family of ruled surfaces in Computer Graphics. The surface parameterization is constructed using the NURBS basis functions and line geometry. The ruled surface is defined by interpolating directly dual unit vectors representing lines, which is a single parametric surface and its shape depends on the control lines. All th...

The isogeometric analysis is a rather new variant of the finite element method (FEM). The key concept of this method is to directly employ a geometric model described by parametric functions as a mesh for the FEM. The models for the isogeometric analysis have been usually based on non-uniform rational B-Splines (NURBS). The applications so far include both twoand three-dimensional models. This ...

Rendering large trimmed NURBS models with high quality at interactive frame rates is of great interest for industry, since nearly all their models are designed on the basis of this surface type. Most existing approaches transform the NURBS surfaces into polygonal representation and build static levels of detail. Unfortunately, algorithms which keep the NURBS representation and generate view-dep...

This work deals with heat conduction problems formulation in the framework of a CAD-compatible topology optimization method based on pseudo-density field as descriptor. In particular, proposed strategy relies, one hand, use Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces to represent and, other well-known Solid Isotropic Material Penalization (SIMP) approach. The resulting is then refe...

Dynamic NURBS, also called D-NURBS, is a known dynamic version of the nonuniform rational B-spline (NURBS) which integrates free-form shape representation and a physically-based model in a unified framework. More recently, computer aided design (CAD) and finite element (FEM) community realized the need to unify CAD and FEM descriptions which motivates a review of D-NURBS concepts. Therefore, in...

In this paper, a new method for constructing NURBS surfaces from scattered and unorganized points is presented. The method is easy to implement and allows fitting a NURBS surface to a scattered point cloud without constructing either NURBS patches networks or polygon meshes. Based on the projection of the points onto the regression plane of the cloud, the method detects both regions where the c...

Based on the potential of current programmable GPUs, recently several approaches were developed that use the GPU to calculate deformations of surfaces like the folding of cloth or to convert higher level geometry to renderable primitives like NURBS or subdivision surfaces. These algorithms are realized as a per-frame operation and take advantage of the parallel processing power of the GPU. Unfo...

A novel adaptive local surface refinement technique based on Locally Refined Non-Uniform Rational B-Splines (LR NURBS) is presented. LR NURBS can model complex geometries exactly and are the rational extension of LR B-splines. The local representation of the parameter space overcomes the drawback of non-existent local refinement in standard NURBS-based isogeometric analysis. For a convenient em...

Dynamic NURBS, or D-NURBS, are a physics-based generalization of non-uniform rational B-splines. NURBS have become a de facto standard in commercial modeling systems because of their power to represent both free-form and common analytic shapes. Traditionally, however, NURBS have been viewed as purely geometric primitives, which require the designer to interactively adjust many degrees of freedo...

This paper presents dynamic NURBS or D NURBS a physics based generalization of Non Uniform Rational B Splines NURBS have become a de facto stan dard in commercial modeling systems because of their power to represent both free form shapes and common analytic shapes Traditionally however NURBS have been viewed as purely geometric primitives which require the designer to interactively adjust many ...